Question

A double slit produces a diffraction pattern that is a combination of single and double slit interference. Find the ratio of the width of the slits (D) to the separation between them (d), if the third minimum of the single slit pattern falls on the fourth-order maximum of the double slit pattern. (This will greatly reduce the intensity of the fourth-order maximum. Assume the central maxima of the single slit and double slit interference patterns are located at the same place on the screen.)

Answer 1

D / d = 3 / 4

Step-by-step explanation:

Let the wavelength and distance of screen be λ and L . Let the distance at which both the fringes fall be at x distance from central point .

For double slit experiment , location of fourth order maxima

x = 4 x λ L / d

For single slit experiment , location of third order minima

x = 3 x λ L / D

As they overlap

3 x λ L / D = 4 x λ L / d

D / d = 3 / 4